The study of waste disposal in deep clay formations requires to better aprehend the hydraulic processes going on in very low permeability layers. In this context, the knowledge of the characteristic parameters of the porous medium (specific storativity, porosity, permeability, etc) is a crucial problem. Geologic porous media are subject to fluctuations of pressure and stress, due to barometric oscillations and to gravimetric fluctuations leading to the phenomenon of « earth tides ». These processes induce hydro-mechanical interactions between the solid skeleton and the pore fluid, both of which undergo deformations under the effect of variable pressure and stress. This paper focuses on the quantitative evaluation of the hydraulic properties of the geologic medium by what might be called informally a "double-barrelled" approach  direct and inverse as explained below. -Direct problem. The governing equations are solved in order to model hydro-mechanically the space-time response of a porous or poro-elastic medium subject to time-variable forcing f(t). -Inverse problem. A stochastic approach is used for identifying the hydraulic characteristics of the geologic medium from observations of piezometric fluctuations. Fluctuations are viewed as random processes, and the direct model is used as a physically-based, spatially distributed type of "input/output" model. (Note: it is also possible to consider a non-stochastic optimization approach). On the other hand, it is assumed in this work that the time series of interest (atmospheric pressure, piezometry, etc) have been submitted beforehand to various statististical treatments and analyses, leading to their characterization in terms of cross correlations and cross spectra : see Fatmi et al. (2007) in this conference. As a preliminary step, we start here with the study of a few prototype problems involving space-time propagation of pressure fluctuations in one-dimension (1D). However, our approach can take into account more generally the 3D geometry of the hypothetical repository, as well as interfaces, heterogeneity, and anisotropy.